Problem: $J$ $K$ $L$ If: $ KL = 8x + 6$, $ JL = 69$, and $ JK = 3x + 8$, Find $KL$.
From the diagram, we can see that the total length of ${JL}$ is the sum of ${JK}$ and ${KL}$ $ {JK} + {KL} = {JL}$ Substitute in the expressions that were given for each length: $ {3x + 8} + {8x + 6} = {69}$ Combine like terms: $ 11x + 14 = {69}$ Subtract $14$ from both sides: $ 11x = 55$ Divide both sides by $11$ to find $x$ $ x = 5$ Substitute $5$ for $x$ in the expression that was given for $KL$ $ KL = 8({5}) + 6$ Simplify: $ {KL = 40 + 6}$ Simplify to find ${KL}$ : $ {KL = 46}$